Related papers: Pluripolar hulls and fine analytic structure

We give an explicit description of commutative post-Lie algebra structures on some classes of nilpotent Lie algebras. For non-metabelian filiform nilpotent Lie algebras and Lie algebras of strictly upper-triangular matrices we show that all…

We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…

We investigate the compatible root graded anti-pre-Lie algebraic structures on any finite-dimensional complex simple Lie algebra by the representation theory of ${\rm sl_2(\C)}$. We show that there does not exist a compatible root graded…

We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characterization of these closed convex hulls is obtained.…

In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…

In this paper we construct for every integer $n>1$ a complex manifold of dimension $n$ which is exhausted by an increasing sequence of biholomorphic images of $\mathbb C^n$ (i.e., a long $\mathbb C^n$), but it does not admit any nonconstant…

Let $\Phi$ be a finite crystallographic irreducible root system and $\mathcal P_{\Phi}$ be the convex hull of the roots in $\Phi$. We give a uniform explicit description of the polytope $\mathcal P_{\Phi}$, analyze the…

Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on "ordinary" amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of…

Let $D$ be a non-pseudoconvex open set in $\C^3$ and $S$ be the union of all two-dimensional planes with non-empty and non-pseudoconvex intersection with $D.$ Sufficient conditions are given for $\C^3\setminus S$ to belong to a complex…

We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…

We prove that the rank-one convex hull of finitely many $2\times 2$ triangular matrices is a semialgebraic set, defined by linear and quadratic polynomials. We present explicit constructions for five-point configurations and offer evidence…

Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra $A$ which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper we…

Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb…

We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact…

We study the geometry of Engel structures, which are 2-plane fields on 4-manifolds satisfying a generic condition, that are compatible with other geometric structures. A complex Engel structure is an Engel 2-plane field on a complex surface…

We study post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic…

This article is devoted to studying multiplicity and regularity of real analytic sets. We present an equivalence for real analytic sets, named blow-spherical equivalence, which generalizes differential equivalence and subanalytic…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…

The pro-algebraic fundamental group can be understood as a completion with respect to finite-dimensional non-commutative algebras. We introduce finer invariants by looking at completions with respect to Banach and C*-algebras, from which we…